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Free planar actions of the Klein bottle group
- Source :
- Geom. Topol. 15 (2011) 1545-1567
- Publication Year :
- 2011
-
Abstract
- We describe the structure of the free actions of the Klein bottle group by orientation preserving homeomorphisms of the plane. This group is generated by two elements $a,b$, where the conjugate of $b$ by $a$ equals the inverse of $b$. The main result is that $a$ must act properly discontinuously, while $b$ cannot act properly discontinuously. As a corollary, we describe some torsion free groups that cannot act freely on the plane. We also find some properties which are reminiscent of Brouwer theory for the infinite cyclic group $Z$, in particular that every free action is virtually wandering.
- Subjects :
- Mathematics - Dynamical Systems
Subjects
Details
- Database :
- arXiv
- Journal :
- Geom. Topol. 15 (2011) 1545-1567
- Publication Type :
- Report
- Accession number :
- edsarx.1101.3137
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.2140/gt.2011.15.1545